Giter Club home page Giter Club logo

optim.jl's Introduction

Optim.jl

Univariate and multivariate optimization in Julia.

Optim.jl is part of the JuliaNLSolvers family.

For direct contact to the maintainer, you can reach out directly to pkofod on slack.

Documentation Build Status Social Reference to cite
Build Status JOSS
Build Status
Build Status
Codecov branch

Optimization

Optim.jl is a package for univariate and multivariate optimization of functions. A typical example of the usage of Optim.jl is

using Optim
rosenbrock(x) =  (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
result = optimize(rosenbrock, zeros(2), BFGS())

This minimizes the Rosenbrock function

$$ f(x, y) = (a - x)^2 + b(y - x^2)^2 $$

with $a = 1$, $b = 100$ and the initial values $x=0$, $y=0$. The minimum is at $(a,a^2)$.

The above code gives the output


* Status: success

* Candidate solution
  Minimizer: [1.00e+00, 1.00e+00]
  Minimum:   5.471433e-17

* Found with
  Algorithm:     BFGS
  Initial Point: [0.00e+00, 0.00e+00]

* Convergence measures
  |x - x'|               = 3.47e-07 ≰ 0.0e+00
  |x - x'|/|x'|          = 3.47e-07 ≰ 0.0e+00
  |f(x) - f(x')|         = 6.59e-14 ≰ 0.0e+00
  |f(x) - f(x')|/|f(x')| = 1.20e+03 ≰ 0.0e+00
  |g(x)|                 = 2.33e-09 ≤ 1.0e-08

* Work counters
  Seconds run:   0  (vs limit Inf)
  Iterations:    16
  f(x) calls:    53
  ∇f(x) calls:   53

To get information on the keywords used to construct method instances, use the Julia REPL help prompt (?)

help?> LBFGS
search: LBFGS

     LBFGS
    ≡≡≡≡≡≡≡

     Constructor
    =============

  LBFGS(; m::Integer = 10,
  alphaguess = LineSearches.InitialStatic(),
  linesearch = LineSearches.HagerZhang(),
  P=nothing,
  precondprep = (P, x) -> nothing,
  manifold = Flat(),
  scaleinvH0::Bool = true && (typeof(P) <: Nothing))

  LBFGS has two special keywords; the memory length m, and
  the scaleinvH0 flag. The memory length determines how many
  previous Hessian approximations to store. When scaleinvH0
  == true, then the initial guess in the two-loop recursion
  to approximate the inverse Hessian is the scaled identity,
  as can be found in Nocedal and Wright (2nd edition) (sec.
  7.2).

  In addition, LBFGS supports preconditioning via the P and
  precondprep keywords.

     Description
    =============

  The LBFGS method implements the limited-memory BFGS
  algorithm as described in Nocedal and Wright (sec. 7.2,
  2006) and original paper by Liu & Nocedal (1989). It is a
  quasi-Newton method that updates an approximation to the
  Hessian using past approximations as well as the gradient.

     References
    ============

    •    Wright, S. J. and J. Nocedal (2006), Numerical
        optimization, 2nd edition. Springer

    •    Liu, D. C. and Nocedal, J. (1989). "On the
        Limited Memory Method for Large Scale
        Optimization". Mathematical Programming B. 45
        (3): 503–528

Documentation

For more details and options, see the documentation

  • STABLE — most recently tagged version of the documentation.
  • LATEST — in-development version of the documentation.

Installation

The package is a registered package, and can be installed with Pkg.add.

julia> using Pkg; Pkg.add("Optim")

or through the pkg REPL mode by typing

] add Optim

Citation

If you use Optim.jl in your work, please cite the following.

@article{mogensen2018optim,
  author  = {Mogensen, Patrick Kofod and Riseth, Asbj{\o}rn Nilsen},
  title   = {Optim: A mathematical optimization package for {Julia}},
  journal = {Journal of Open Source Software},
  year    = {2018},
  volume  = {3},
  number  = {24},
  pages   = {615},
  doi     = {10.21105/joss.00615}
}

optim.jl's People

Contributors

ahwillia avatar alyst avatar andreasnoack avatar anriseth avatar antoine-levitt avatar arnostrouwen avatar benkuhn avatar bicycle1885 avatar blakejohnson avatar blegat avatar briochemc avatar chrisrackauckas avatar cortner avatar cossio avatar evizero avatar femtocleaner[bot] avatar github-actions[bot] avatar gwater avatar jeff-regier avatar johnmyleswhite avatar kristofferc avatar lindahua avatar mcreel avatar mlubin avatar pkofod avatar rsrock avatar tcovert avatar timholy avatar tkf avatar yuyichao avatar

Watchers

 avatar

Recommend Projects

  • React photo React

    A declarative, efficient, and flexible JavaScript library for building user interfaces.

  • Vue.js photo Vue.js

    🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.

  • Typescript photo Typescript

    TypeScript is a superset of JavaScript that compiles to clean JavaScript output.

  • TensorFlow photo TensorFlow

    An Open Source Machine Learning Framework for Everyone

  • Django photo Django

    The Web framework for perfectionists with deadlines.

  • D3 photo D3

    Bring data to life with SVG, Canvas and HTML. 📊📈🎉

Recommend Topics

  • javascript

    JavaScript (JS) is a lightweight interpreted programming language with first-class functions.

  • web

    Some thing interesting about web. New door for the world.

  • server

    A server is a program made to process requests and deliver data to clients.

  • Machine learning

    Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.

  • Game

    Some thing interesting about game, make everyone happy.

Recommend Org

  • Facebook photo Facebook

    We are working to build community through open source technology. NB: members must have two-factor auth.

  • Microsoft photo Microsoft

    Open source projects and samples from Microsoft.

  • Google photo Google

    Google ❤️ Open Source for everyone.

  • D3 photo D3

    Data-Driven Documents codes.